 so that we at least one see each other today. So end of the coffee break, please come back early. And people online, please switch on your camera. So our next speaker is André Benassi, who is coming to us from the real world, where scientific excellence supports economic growth directly, hopefully. And he will talk about powders in pharmaceutical industry. Hopefully. So thank you, Roland. And of course, a great thanks to the organizers for inviting me here and from time to time being able to share my results with you. And yeah, today I want to show you some experimental results we measured recently about a couple of different topics that I can manage. No? Use the pointer. No? OK, so let me use the mouse. So about a couple of topics, both of them related to powder mechanics. And so we're talking about mesoscale sliding and mesoscale dissipation phenomena. We are talking about from few to many hundred micron size particles. And I hope to convince you that in this powder mechanics, we still see some open issue, which is from one side is preventing us from reaching a complete understanding and predictivity and predictive model helping us in our daily activity of designing processes and products. But on the other side, there is still some fun to play because we believe there is still some basic mechanics to be unraveled. And the first topic has to do with the study, the behavior of the shearing behavior of confined powders. Why we're interested in these kind of things in our work, we typically have to design the different, say, geometrical or mechanical objects like uppers, silos, funnels, dosator, steering system, which means objects that are confining a powder in a given geometry and they are supposed to let it flow in a certain way, or objects that are moving inside the powder. And so you have to avoid phenomena like you see in the upper right corner, clogging phenomena, funnels, or you have to prevent this buildup formation in the mobile part that are moving in the powder. And to do this, there are a lot of, let's say, empirical engineering receipts. And the Schünze book, it's quoted up there, is a sort of Bible in this field. But all these techniques start from the bottom line that you are supposed to know or to be able to measure the so-called yield locus of a powder, which is nothing but a friction force versus load plot. Pretty much like you have seen also in many presentations you can obtain with a confined lubricant under shear or even just sliding a solid object on a substrate. So what we do, we confine our powder bed in gray up there with applying a normal sigma stress. And then we let the slider move and we record the tau force, the shear stress, which the powder is exerting to resist the motion. At some point, the powder will no longer able to resist. And so there will be the nucleation of a shear band in the middle of the powder bed and the upper part, which we slide. And so we call this the tau max value, which is the equivalent of the friction force. And if we plot friction force versus sigma, we all know we have to expect this straight line behavior, whose slope you call the friction coefficient in the community of powders. This is called the angle of internal friction. And the complication of powders compared to liquids or solids is that the powders retain memory of the way you have prepared them, of the way you prepare the sample and the way you have treated the powder before making the measurement. So if you just put a powder in a container, you will end up having what we call the weak consolidation state, which is basically a situation where there is no large number of coordination for the particles. There is not such a big packing. The powder incorporates a lot of air. And in this condition, the powder can offer a certain resistance to friction. And then if you have granular material, it's enough that you shake it a little bit and you allow the powder particle to sit more conveniently and you increase the consolidation state, the coordination number, the density. Or if you have a powder, typically shaking it's not enough, so you have to apply a vertical compression to condition the powder to a certain consolidation state. And then, of course, you can perform your measurements. And so for a powder, it's not enough to characterize the sliding behavior. It's not enough to measure a single curve, but we have to measure a family of curves, depending on the pre-consolidation state in which we prepare the sample. How this is done in practice, it is not, of course, a one-dimensional slider. But in practice, we have on the left corner, we have this movie showing this shear cell, which is nothing but a cylindrical couvet that we fill with powder. You see it in the bottom of the movie. And then we have a piston, which is pushing the powder vertically. And then we can rotate it at constant velocity. You don't see the rotation because we are talking about few degrees per minute, so I should have accelerated the movie to let you see it by naked eye. And so what we do, we pour the powder in green up there. We then apply vertical load to pre-consolidate the powder to a given state. And then we start rotating at constant velocity. And we measure both the normal load that we are supposed to apply, and also the resistance torque that the powder is exerting to the rotation. Up to the point, of course, where we have the shear band formation. And so we record the tau max value, the frictional force for the powder to slide. It's important to mention that below the piston, the surface is not flat, but we have a few millimeter thick blades. Because when we push the piston, it has to grip the powder so we can make sure that the shear band is generated inside the powder bed and not between the powder bed and the smooth steel piston. We can also do something better. We can keep recording sigma and tau, even after the instrument gave us the value of tau max. And so we can keep recording in time what is going on. And we discovered that in most of our sample, we see a sort of stick slip behavior, a SO2 profile. Because basically, initially, the powder cylinder will deform elastically, like a rigid body, after the creation of the shear band, the upper part will slide forward. But then the energy in the shear band is dissipated. The shear band disappear. And so again, for a moment, the powder bed will deform elastically up to the next shear band formation. So we have this SO2 profile that we will analyze in a couple of slides. One slide about the motivation and the kind of powder we are using and what we want to do. The point is that these real world commercial pharmaceutical powders, they come in a very disordered condition. So they are not ideal monodisperse powder. And at least we can define three main variable to characterize the powder. One is indeed what we call the DV50, so the average, the median particle diameter. And we have many samples tested in this work. We concentrated on a single material, lactose. And all the data are in that paper down there by Giulio Cavalli et al. So we analyzed very different commercially available powder from a few micron in average diameter up to many hundreds, 350, 400 micron particle size. But typically, the average particle size is not enough. All these powder are very polydispersed. And we can measure this polydispersion. You see some curve there. You can regard this log normal distribution really as a probability distribution function to have a certain diameter in your powder. And so you see typically the DV50 coincides with the central peak, but then there is a certain dispersion around this average value. And plus, maybe you can find different powders having roughly the same particle characteristics, but they can have a very different shape. So some lactose powder, they come from crystallization. So they come down in the form of a single crystal with this tomahawk shape that you find in the second row. Then we can fuse together the tomahawk and we can create very irregular particles that you see in the third row. Or you can use spray drying or other particle engineering techniques. You can dry up lactose, which is initially in solution in a droplet. So as a result, the particle will be perfectly spherical, like the initial droplet. It's very spherical, but it could be porous and a little bit rough on the surface. And lastly, you can even mesh this powder particle and create very, very small fragments, a few micron size, so very irregular, very small fragments. So the point is, every time that we try one of these new powders in our plants, we should measure not one, but many different curves. And these experiments are time-consuming, so we ask ourselves, is it possible in principle to measure maybe the characteristics for all these powders, the heat locus for all these powders, but then finding an analytical expression to fit simultaneously all these equations with some fitting parameter inside, which, of course, we expect to depend on the size of the particle, a shape factor, and maybe about the point dispersion factor. So we started and we did it. And we performed many different heat locus plot at different pre-consolidation states. And we found that out of 10 different possible equation more or less found in literature, only two of them are able to fit simultaneously all the data for all the lactoses and for all the different pre-consolidation states. And those are the two shown in the right side. And there are two main fitting coefficients here, C and T. And the first surprise, which is something I'll explain, one of these open issues that I'm discussing with you, hoping to puzzle you and to have some answer or some possible joint collaboration to understand it, is that this coefficient, they don't depend at all on the shape of the particle. They depend mostly on the average particle size distribution, very, very weakly on the amplitude of the dispersion of the particle size distribution. So they depend mainly on the dv50. And this is an open point. In principle, we have our now predictive equation. So if I buy a new lactose and I measure the dv50 with that equation, I can predict the shape of the heat locus plot. And in principle, we could be happy. But we are also curious. And so as a funny game, we also had a look to the stick slip that we record after the first slip event in the shear set. And my first point is, is it really a stick slip? My first concern was, is it really a stick slip? Maybe is it an artifact of the shear set instrument? And so what I did, I compared the characteristics of the SO2 profile with the prescription by Thomas Somm model or Franklin Contrava model. And this model, they basically tell you that the shear force and the normal force in standard condition, they should oscillate perfectly in phase. And this is shown in the first plot for one of our samples in the blue and red curve. You see normal lateral force that are oscillating in phase. The model prescribed that if you unload the sample, the slider, the amplitude of the stick slip should decrease. And this is shown in the bottom left panel where you see moving from blue to pink curve. We are unloading the sample and the amplitude is decreasing. And also another prescription is that if you start sliding faster and faster, basically initially you have a SO2 profile which is very asymmetric, maybe triangular shape. But then it becomes more, let's say, more symmetric, more sinusoidal-like. And this is what we see in the other bottom panel where you see in blue a typical triangular SO2 profile at very low velocity. What is it, 8 degrees per minute. And when we go to 18 degrees per minute, you will see the stick slip becomes more sinusoidal. Now again, another kind of surprise, which is it seems to be a stick slip, but what is the stick length? There is somebody which is not on mute. Is it me? No. And now it's fine. So what is the characteristic slip length? And is there in principle that there should be or not the characteristic length? Because this is not a one-dimensional sliding system. We have a rotating system, and if you think what the particle are doing during rotation, they move along an arch length which is a different length depending on how far you are from the main rotational axis. So in principle, particles are displacing during slip at totally different lengths. So why there should be a characteristic length? This is still not clear to me, but indeed, it is there. Because if you look in the upper right corner, you see one blue cube, which is a stick slip, has a function of the length now, that the arch length that the piston is drawing. In blue is for our courses particles. So for our courses, in powder, we have 350 micron particle size. And in the yellow case, we have the smallest particle size, a few micron particle size. In both cases, stick slip is there. I would have expected to see it more irregular. And instead, it's very, very regular. And there is some characteristic length, which is in principle dependent on the particle size because it's smaller in the yellow case and larger in the blue case. But it's difficult for us to have a predictive, let's say, model which is allowing us to understand and to predict which is this characteristic size. And then we also measured the slip time and the stick time. And again, there is not a surprise. The slip time does not depend at all, neither on the particle size nor on the particle shape. You see the scale, it's very small. So it seems a scattered plot, but it's 0.2 or 0.8. So it's roughly constant, and it does not depend on anything. Whereas the stick time has a linear increase, which is, again, OK, with Tomlinson because you can imagine that if you have a larger particle, the washboard potential in Tomlinson is deeper. And so it takes longer time to the pin from a minimum. But then at some point, it seems to go to a plateau. Here, the data are very scattered. So it's just a suggestion, which is definitely something we have to investigate more. And again, also for this point, we don't have a very deep explanation. So it would be nice maybe to investigate these things with molecular dynamics or with discrete element modeling, where you can also introduce a shape for the particle, which are not pointy object, but they can become, let's say, more irregular particles, or maybe, experimentally, scaling up the problem using a larger particle like silica beads. Which you can buy in very narrow distribution so you can combine them. And you can create your, let's say, model powder, where you can continuously modify the dispersion and particle size and whatever. And this is basically the first topic. Second point I want to discuss with you is a second application is about breaking particles. So for many of our application, we need to smash the particle into smaller fragments. One reason out of many is, for instance, in our product for inhalation, we ask patient to inhale a dry powder and few milligram, and this powder particle are supposed to deliver the active principle into the alveoli, which is the terminal part of the human lungs. But human lungs works as a filter for particle, and so the only way for particle to escape this filtering action is to be in the range between one and three, one and five micron. So typically we buy powder that are coarser or we synthesize our own powder that comes with particle size determined by the thermodynamic of the reaction and we cannot control it specifically. And so we have to break them into smaller fragments. This is done in pharmaceutical application in jet mills, which is the object you see up there, side view and top view, and basically a jet mill is a sort of another chamber, 10 to 30 centimeter in size, depending on the plant. There are some lateral nozzles here, here and here, where you basically inflate a high-speed gas like nitrogen or dry air, and it's a supersonic object because mach inside it's 1.5 up to two. The outlet for the gases in the central part is the central tube you see there. So we create a vortex of supersonic gas, which is rotating, and when you put the powder in, the powder is entrained in this vortex and it starts to rotate, and the centrifugal force is pushing the particle to the peripheral wall chambers of the wall, and here is where the particle is supposed to have a lot of collisions and break into fragments. When the fragments are small enough, the drag force exerted by the gas moving out overcome the centrifugal force and then the particle are able to rotate towards the center via spiral trajectories, and finally they are collected in the outlet pipe. So this is the way we classify only very, very fine fragments. And you see down here the characteristic experiment we can do, we put in the mill a powder which is characterized by the black line, the starting material, so the powder with a very big poly dispersion and 10 to 11 micron in size as an average diameter, and after milling, if we measure it, you see that the particle size distribution is less shifted and now the dv50 is around, so the average particle diameter is around two, three microns, and it's also sharper, so it's less poly dispersed. And so this is a good outcome of the jet wing. You see many curbs here because one of the parameters we can play with this kind of process is the pressure of the gas. So in principle, the stronger the pressure, the faster the gas, more violent the collisions, and you could, in principle, left shift a little bit more the particle size distribution. Now, this material, this movie, by the way, come from some simulation we did that are published in that paper down here. It was a first attempt for us to build up a predictive model for this operation. And we need a predictive model because the powder that we are milling are very expensive from 60 to 80,000 euro per kilogram, and they come from the synthesis reactor in few kilograms. So if you use trial and error procedure to set up this process, we consume alpha kilo, which is, you understand, very, very embarrassing and definitely not convenient, so the idea would be to have a predictive tool. Simulation are too complex because we have supersonic fluid, compressible fluid, all the particle mechanics that you have to put in the equation, it's very messy, so it was a first attempt. Our second attempt was, let's try to make an empirical connection. So let's measure something on the single particle, some mechanical properties of the single particle, doing indentation, classical indentation experiment that people interested in fracture mechanics they know very well. And then let's try to make a connection between the microscopic properties we measure on single particle and the behavior of the powder during milling. So what we do typically, we glue a single powder particle on a glass sample holder and then we put it under a micro-indenter with a tip, which is basically many micro-large insides, much, much bigger than an AFM tip. We control the vertical load Pmax, you see in blue up there, and we push it down, and during the approach and retraction, we measure of course, the force versus penetration fluid. And we can also then we have a tabletop AFM besides and we can image the footprint of the indentation just after the indentation. And you see an example here. So you see it's a very few micro-wide indentation footprint and we can also measure the crack length, which is an important element. There are cracks that are departing from the edges of the footprint. Here there is also one which is crossing the whole footprint, which should not be there, but sometimes it happens. And with all this quantity, basically with the crack length and the information in the hysteresis loop, we can calculate all these quantities. The hardness, which is of course the normal force divided by the area that you create in the footprint, which is of course, if you know the shape of the indenter, it's proportional to the penetration depth simply. And the hardness is an index telling you how prone is a material to undergo a plastic deformation, whatever kind of plastic deformation. The harder and the more difficult is to to plastically deform a particle. Then there is the Young Modulus, which doesn't need an introduction. Here we calculate it as the slope of the hysteresis loop. Then when you have both of them, and if you measure the crack length C, you can calculate the fracture toughness, which is also a stress, dimensionally speaking. And it's basically the maximum stress that you have to overcome before you have the free irreversible propagation of the crack in your material. So when you overcome that stress, crack propagates freely and they propagate through the whole length of the particle, fragmenting the particle into smaller pieces. So the smaller, the better. It means that we have to apply less stress to the particle to generate fragments. And even more instructive is if you plot H over K, which we call the Brittle's index, because this quantity, when it is very big, particles will be very prone to get fragmented by Brittle, fractured by crack propagation, because Kc means it's very small, so B goes up. On the contrary, when B is very small, this could be because Kc is huge, so you need a huge stress in your particle to initiate the crack propagation, so that particle is not prone to break by Brittle fracture, or even because H is still small, so the material is prone to deform, but not by Brittle fracture, which means that it can only deform by ductile deformation. So again, we would like to have large B for our material in our jet means. Final quantity that you can calculate with a bit of modeling and assumption underneath is the so-called critical size, which is basically the smallest size of a sample or a particle that you can obtain before you see the ductile to Brittle transition. So at some point, if you load your particle, there is, I mean, you will never succeed in reaching the stress to propagate the crack before you start deforming plastically the particle. So this is basically a lower limit for us because this is for us the smallest fragment attainable in a jet wheel. If you keep milling a particle with size equal to DC, it will plastically deform on the surface, so it will become like the moon with a lot of craters on top. Maybe some material will amorphize on the surface, but you will never succeed in breaking it into smaller pieces. So we calculated all these quantities for some compound of interest for us, like again lactose, tartaric acid, sodium chloride, and you see compound ABC, that these are compound of our synthesis that don't still have a name, and we table all this parameter and then we put the same sample in a jet mill and we perform some milling trial. You see in black, in every plot you see in black the starting material particle size distribution and correspondingly in colored curve you see the left shifted distribution after milling. And you see for instance for compound B and C it's very, very easy to perform milling. Very easily, no matter what pressure you apply the distribution immediately left shift and you have very narrow and very small particle size but other material like sodium chloride or tartaric acid are much harder and even if you push the pressure up to the maximum value you do not succeed. So we wanted to see is it possible to link the two aspects and basically we found that the quantity which is correlating best with the experiment is the Brittenek's index. And here you see the correlation of Brittenek's index with the DV9. The DV9 is basically the ninth percentile of this distribution. So the diameter below which lie 90% of the area of your when you integrate the distribution. So if you want it's proportional to where the right shoulder of the distribution sits. And you see here when you increase the Brittenek's index it's easier to shift the distribution to the left. So it's easier to obtain smaller fragments. Of course to have fully predicted theory we would like also to predict where the right shoulder of the peak, sorry where the left shoulder of the peak is. So the smallest fragment attainable will lie. So that basically would be nice now when we have a new material we do some indentation test, we measure B and from those fitting black lines that you see there we can predict what to expect in the million properties. And this is a problem because if we want now to look which is the smallest fragment size using the equation I showed you before this DC equation it fails completely. And you see the value of DC calculated for the different material are the colored dots and the experimental finding is the continuous bottom line the dot dashed line. So in all the experimental sample we see particle fragments up to 0.2 microns and this is in agreement with the theory for compound B and C but for all the other compounds the theory would predict one or two orders of magnitude overestimation of the particle size. God knows why. We are not the only one reporting this failure there are some speculation literature and one possibility is that to calculate this equation to calculate DC you do a lot of assumption on which kind of crack mode is propagating and how it propagates beneath the indenter tip which is maybe not so controlled condition when you have this fast particle that are cracking in the jet mill. So it's a very dynamical situation and not a quasi static control crack. And as far as we know, there is no theory which is basically helping us in this task. And yeah, more or less I think this is all we also define the sorry, a grand ability index which is just a way of classifying all the powders in terms of how easy will be to mill them and all the material except Atari cases they are perfectly linearly aligned on the fitting function which is also a nice result. But yeah, that's more or less it, thank you. Indeed, a truly industrial talk where we have compound A, B and C and are not supposed to know what it is. Good for physics, bad for material science. I don't know either. I got them from our chemist and I don't wanna know anything. I just look at the particle under the microscope. Thank you Andrea, I wanted to ask after milling you got this side distribution which becomes left shifted which is intuitive let's say but also I've seen a second peak which maybe is not so intuitive. This is very interesting and the point is why you need some simulation typically because this is a very non-linear phenomena and basically I told you before the moment where the particle are classified out of the mill it depends on the balance between centrifugal force and the drag force, okay? But the drag force depend on how fast is the fluid, okay? And then there is this feedback because if you are not milling efficiently and you are keeping putting powder in you increase the amount of powder you will slow down the fluid so even the drag force and the centrifugal force will change the balance and so you will end up putting more or less particle out. So there is an indirect feedback which makes the thing complicated. And for instance in the upper part there you see PD dispersion or whatever it is that you put powder in and this you can do continuously in a plant you cannot do it stop and go it's a continuous flow in a large industrial plant and put the powder in and the powder is very hard so it accumulates a lot of material inside the mill the mill velocity, the gas velocity is reduced and then all the milled puke out all the powder with the same size it was entering in. Then after puking the mill becomes empty and it becomes again faster and faster so part of the material which was not puk is finally milling in the correct way and this is why we have these alternations sometimes it pukes big material some other cases it works correctly and it's an intermittent behavior. Question here? I have a question about the stick slip which you observed maybe you have actually melting of the system and that happens for example in breaks when you have a break squeal so basically the system heats up or you have probably waves propagating through your system and they act as temperature and they melt this system and then it shears easier and then the energy is dissipated there is no more waves to be generated and propagate and then it freezes back and this would create also such a... It's very very gentle mechanical motion we don't even touch the powder or measure in temperature we don't see any change in temperature It's just waves propagating back and forth when they heat particles they generate waves, oscillations, vibrations which propagate through your system not temperature but... It's difficult to verify anything because if you look at the powder closely it's just white even if we have a fast camera I try for instance to measure the amplitude of the shear band because also literally I found anything concerning how big is the shear band and how does it depend on the particle size as well I try to put some black powder and to use it as a marker and see if I was able to see something I'm sort of... No, no, go ahead but I'm just wondering probably John can talk for two hours about crack propagation and small particles I'm not going to just a quick comment because it's really nice work, thank you the kinetic energy of the particles arriving at the surface or anywhere where the impact is going to be important just a quick question for you the torsion measurements you make of course have different strain rates have you tried varying the radius of the torsion test or is that just too much? You mean in the shear cell experiment? What do you mean? We use the standard cuvette from the instrument but it could be nice to... We can manufacture our own one and the instrument is very easy Good suggestion Okay, let us thank Andrew again for sharing these results with us and the ideas how to move on